Related papers: Buildings for Synthesis with Clifford+R
We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…
Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as $T$, are particularly expensive due to…
In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
Matchgate unitaries are ubiquitous in quantum computation due to their relation to non-interacting fermions and because they can be used to benchmark quantum computers. Implementing such unitaries on fault-tolerant devices requires first…
The matrices that can be exactly represented by a circuit over the Toffoli-Hadamard gate set are the orthogonal matrices of the form $M/ \sqrt{2}{}^k$, where $M$ is an integer matrix and $k$ is a nonnegative integer. The exact synthesis…
In this paper we study single qutrit circuits consisting of words over the Clifford$+D$ cyclotomic gate set, where $D=\text{diag}(\pm\xi^{a},\pm\xi^{b},\pm\xi^{c})$, $\xi$ is a primitive $9$-th root of unity and $a,b,c$ are integers. We…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C\dag$, using ancilla qubits and measurements. The procedure uses ancillary $|+\rangle$ states,…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary…
We describe a new method for the decomposition of an arbitrary $n$ qubit operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators where $n\le…
The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T gate, an…
We give a presentation by generators and relations of the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$ of unitary $4\times 4$ matrices with entries in the ring $\mathbb{Z}[1/\sqrt{2},i]$. This is motivated by the problem of exact synthesis for the…
It is known that the matrices that can be exactly represented by a multiqubit circuit over the Toffoli+Hadamard, Clifford+$T$, or, more generally, Clifford-cyclotomic gate set are precisely the unitary matrices with entries in the ring…
Prevailing proposals for the first generation of quantum computers make use of 2-level systems, or qubits, as the fundamental unit of quantum information. However, recent innovations in quantum error correction and magic state distillation…
Clifford circuit optimization is an important step in the quantum compilation pipeline. Major compilers employ heuristic approaches. While they are fast, their results are often suboptimal. Minimization of noisy gates, like 2-qubit CNOT…
We present a novel architecture-aware transpilation method for exact general unitary gate synthesis on superconducting quantum hardware. Our approach is tightly integrated with the optimized block-ZXZ decomposition, exploiting its recursive…
Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…
In this paper we prove a collection of results on the structure of permutations in the Clifford Hierarchy. First, we leverage results from the cryptography literature on affine equivalence classes of 4-bit permutations which we use to find…